Leibniz MMS Days 2023 - Abstract
A cell-centered multigrid approach for the semi-implicit integration of acoustic systems is presented. The approach can be also adopted to solve the pressure Poisson-equation arising in incompressible flows. Particular features of the discretization include a representation of physical boundaries by cut cells, a block-structured Cartesian grid to enable local refinements, and a parallelization strategy based on generalized Hilbert space-filling curves. As the cut-cell discretization leads to operators with strongly varying/discontinuous matrix coefficients, important considerations for good multigrid convergence include the representation of the discontinuities on the coarse-level grids. We found that crucially important are also modifications to the standard constant/trilinear restriction/prolongation operators to respect the discontinuities. In the exceptional case when these considerations still fail to achieve the desired convergence rate, a promising option to boost convergence can still be to use the multigrid algorithm as a preconditioner for the biconjugate gradient stabilized algorithm.